The shooter in the UK was a licensed owner. So of course the next calls will be to ban shotguns (and probably airguns) entirely.
What this shows though, is that no matter how strict the laws, someone going nuts will find a way to do it. Arbitrary licensing, expensive registration, outright bans... All of it failed and will continue to fail.
It's a good thing we have organizations like the NRA, SAF, CCRKBA etc. here in the US or we would be in the same boat the Brits are right now.